There is no spa at AKL. They have a fitness center and you can get massages, but that's it. The spas are at Grand Floridian and Saratoga Springs -- both are wonderful and listed on the site given by the last poster.
Hmmm -- on second glance, maybe I'm wrong. When we last stayed almost 2 years ago all they had were massages, but relaxedyet.com seems to say otherwise. I'd call to be sure.
Yes, AKL does offer massage, body wraps, and facials. The locker rooms have steam room and sauna, but no whirlpool. It it IN the fitness center, but a little more spa-like than other fitness centers on property.